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Started by Staffan Asplund AT
Mon, 02 Nov 1992 13:50
planning of experiments
Author: Staffan Asplund AT
Date: Mon, 02 Nov 1992 13:50
Date: Mon, 02 Nov 1992 13:50
60 lines
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2448 bytes
Hello,
A question about which critera to use when doing experimental planning.
A test plan that can be used without 'a priori' knowledge about
the model structure
is a plan with as low correlation between the independent variables as
possible.
In the literature this type of plan is perhaps considered to simple
for discussion.
I would like to get some pointers to literature stating that a minimum
correlated testplan is a good approach if the model structure is UNKNOWN.
A group of people here at my laboratory is talking in favor of using
a critera of the following kind:
maximum ( determinant( transpose(X) * X ) )
where X is a ( m * n ) matrix with m experiment and n variables.
It can be shown that this method minimizes the coovariance of the
parameterestimates.
BUT if this criteria is used there can exist coovariances between
undependent variables up to 0.2 or 0.3 in our examples, compared to
a max of 0.04 when using
minimum( biggest element in coovariance matrix )
as criteria.
MY QUESTIONS:
1. References or comments on giving the coovariance between independent
variables in a testplan high priority ?
2. What's Your criteria when planning tests for unknown modelstructures?
Post or mail, whatever You prefer.
I will summarize Your comments if they are not posted to the newsgroup.
All comments appreciated,
Staffan
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- Project researcher / Environmental Engineering -
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- Staffan Asplund - email sasplund@abo.fi -
- Process Design Lab. - phone +358-21-654552 -
- Abo Akademi University - ph. home 921-882744 -
- Finland - fax +358-21-654791 -
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Re: planning of experiments
Author: Donald E. Ramirez
Date: Mon, 02 Nov 1992 15:48
Date: Mon, 02 Nov 1992 15:48
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In article <1992Nov2.135009.29552@abo.fi> SASPLUND@finabo.abo.fi (Staffan Asplund AT) writes: >A question about which critera to use when doing experimental planning. >A group of people here at my laboratory is talking in favor of using >a critera of the following kind: > maximum ( determinant( transpose(X) * X ) ) > The D-optimality criterion is based on the product of the eigenvalues of (X'X)**(-1) and is small when only one of these eigenvalues are small. A new criterion is based on the mean standard error of a random test of u'b; that is the expectation over the unit sphere of a random linear inference. This is equivalent to looking at the (1-alpha) confidence region for the b's and computing the mean shadow of the ellipsoid in a random direction. The problem of computing the mean radius of an ellipsoid is numerically equivalent to computing the surface area of an ellipsoid, which had been a long-standing problem for p>=4. This problem has been recently solved by Charles Dunkl and Don Ramirez of the University of Virginia and will appear in The Transactions of Mathematical Software ACM. Their code produces the surface measure of an ellipsoid and the mean radius which is equivalent to the new criterion for choosing optimal designs given above. The code is in Fortran and is available from der@virginia.edu. -- * Don Ramirez * Dept. of Mathematics * I would * * der@virginia.edu * University of Virginia * rather * * (804) 924-4943 * Math-Astronomy Building * be in * * (804) 982-3084:fax * Charlottesville, VA 22903 USA * Antigua *
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